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Theorems · Theorem · global analysis

Differentiable.neg

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F},
  Differentiable 𝕜 f → Differentiable 𝕜 (-f)
Defined in
Mathlib.Analysis.Calculus.FDeriv.Add
Cited by
6 results in Mathlib
Foundations
Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

differentiable_neg · cited by 5differentiable_negPhragmenLindelof.horizontal_strip · cited by 3PhragmenLindelof.horizont…Differentiable.fun_neg · cited by 2Differentiable.fun_negComplex.HadamardThreeLines.diffContOnCl_invInterpStrip · cited by 1HadamardThreeLines.diffCo…differentiable_fun_neg_iff · cited by 0differentiable_fun_neg_iffdifferentiable_neg_iff · cited by 0differentiable_neg_iffNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldDifferentiable · cited by 298DifferentiableDifferentiableAt.neg · cited by 7DifferentiableAt.negDifferentiable.negCITED BYCITES

Cites5

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Cited by6

Results whose statement or proof uses this declaration.